scholarly journals Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Alejandro Marquez ◽  
Jairo José Espinosa Oviedo ◽  
Darci Odloak
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Linear Model ◽  
Predictive Control ◽  
Linear Time ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Operating Condition ◽  
Order Linear ◽  
Proper Orthogonal ◽  
Low Order

This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor.

Temporal evolution analysis of in-cylinder flow by means of proper orthogonal decomposition

2020 ◽  
pp. 146808742091724
Author(s):  
Li Shen ◽  
Kwee-Yan Teh ◽  
Penghui Ge ◽  
Fengnian Zhao ◽  
David LS Hung
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Internal Combustion Engines ◽  
Temporal Evolution ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Temporal Behavior ◽  
Decomposition Approach ◽  
Cylinder Flow ◽  
Proper Orthogonal ◽  
Low Order

In-cylinder flow fields and their temporal evolution have strong effect on the combustion dynamics of internal combustion engines. Proper orthogonal decomposition is a statistical tool to analyze these flow fields by decomposing them into flow patterns (known as proper orthogonal decomposition modes) and corresponding coefficients with their contribution to the ensemble flow kinetic energy successively maximized. However, neither of the two prevailing proper orthogonal decomposition approaches satisfactorily describes the temporal behavior of the flow fields. The phase-dependent proper orthogonal decomposition approach is limited to analyzing spatial flow structures at a certain engine phase. The phase-invariant proper orthogonal decomposition approach attempts to account for both spatial and temporal variations, but at the expense of diminished statistical and physical significance. In this article, we seek to understand the temporal behavior of tumble flow fields by analyzing the evolution of low-order phase-dependent proper orthogonal decomposition modes over multiple crank angles. The concept of relevance index is first generalized to enable comparison between two vectorial fields of different sizes. This metric is then used to quantify the directional similarities between the two lowest proper orthogonal decomposition modes obtained at sequential crank angles. The mode shapes are observed to evolve gradually and naturally over most crank angles, but change significantly at certain crank angles during intake. The results indicate that each of the low-order modes features strong velocity fluctuations in different regions of the tumble plane, and different numbers of modes are needed to represent the dominant features of tumble flow at different engine phases. Based on this understanding, we propose to use the partial sum of those proper orthogonal decomposition modes and their coefficients to form a low-order approximation model of the in-cylinder tumble flow, in order to reduce flow field complexity and noise while retaining its major spatial and temporal features.

Nonlinear Modeling of Mechanical Gas Face Seal Systems Using Proper Orthogonal Decomposition

2006 ◽  
Vol 128 (4) ◽  
pp. 817-827 ◽  
Author(s):  
Haojiong Zhang ◽  
Brad A. Miller ◽  
Robert G. Landers
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Initial Conditions ◽  
Nonlinear Modeling ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Face Seal ◽  
Reduced Order ◽  
Wide Range ◽  
Gas Face Seal ◽  
Proper Orthogonal

An approach based on proper orthogonal decomposition and Galerkin projection is presented for developing low-order nonlinear models of the gas film pressure within mechanical gas face seals. A technique is developed for determining an optimal set of global basis functions for the pressure field using data measured experimentally or obtained numerically from simulations of the seal motion. The reduced-order gas film models are shown to be computationally efficient compared to full-order models developed using the conventional semidiscretization methods. An example of a coned mechanical gas face seal in a flexibly mounted stator configuration is presented. Axial and tilt modes of stator motion are modeled, and simulation studies are conducted using different initial conditions and force inputs. The reduced-order models are shown to be applicable to seals operating within a wide range of compressibility numbers, and results are provided that demonstrate the global reduced-order model is capable of predicting the nonlinear gas film forces even with large deviations from the equilibrium clearance.

Prediction of Transient Thermal Behavior of Planar Interconnect Architecture Using Proper Orthogonal Decomposition Method

2011 ◽  
Author(s):  
Banafsheh Barabadi ◽  
Yogendra K. Joshi ◽  
Satish Kumar
Keyword(s):  
Thermal Behavior ◽  
Proper Orthogonal Decomposition ◽  
Joule Heating ◽  
Computational Cost ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Fe Model ◽  
Inhomogeneous System ◽  
Transient Thermal ◽  
Proper Orthogonal

A major challenge in maintaining quality and reliability in today’s microelectronics devices comes from the ever increasing level of integration in the device fabrication as well as the high level of current densities that are carried through the microchip during operation. Cyclic thermal events during operation, stemming from Joule heating of the metal lines, can lead to fatigue failure due to the varying thermal expansion coefficients of the different materials that compose the microchip package. To aid in the avoidance of such device failures, it is imperative to develop a predictive capability for the thermal response of micro-electronic circuits. This work studied the problem of transient Joule heating in interconnects in a two-dimensional (2D) inhomogeneous system using a reduced order modeling approach of the Proper Orthogonal Decomposition (POD) method and Galerkin Projection Technique. This study considers an interconnect structure embedded in the bulk of a microelectronic device. The effect of different types of current pulses, pulse duration, and pulse amplitude were investigated. By using a representative step function as the heat source, the model predicted the exact transient thermal behavior of the system for all other cases without generating any new observations, using just a few POD modes. To validate this unique capability, the result of the POD model was compared with a finite element (FE) model developed in LS-DYNA®. The behaviors of the POD models were in good agreements with the corresponding FE models. This close correlation provides the capability of predicting other cases based on a smaller sample set which can significantly decrease the computational cost.

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